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Strong stability and the Cayley transform

Halikias, G. (2014). Strong stability and the Cayley transform. Mathematical Methods in the Applied Sciences, 37(2), pp. 212-216. doi: 10.1002/mma.2976


The general notion of 'strong' stability for internal autonomous system descriptions has been recently introduced for continuous and discrete-time systems. This is a stronger notion of stability compared with alternative definitions (asymptotic, Lyapunov), which prohibits systems described by natural coordinates to have overshooting responses, for arbitrary initial conditions in state space. The paper reviews three refined notions of strong stability, along with the necessary and sufficient conditions corresponding to each notion. Using the Cayley transformation, it is shown that the notions in the two domains are essentially equivalent and that the strong stability conditions can be transformed from one domain to the other in a straightforward way.

Publication Type: Article
Additional Information: This is the peer reviewed version of the following article: Halikias, G. (2014), Strong stability and the Cayley transform. Math. Meth. Appl. Sci., 37: 212–216., which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Publisher Keywords: Strong stability, Cayley (bilinear) transformation
Subjects: T Technology > TK Electrical engineering. Electronics Nuclear engineering
Departments: School of Science & Technology > Engineering
School of Science & Technology > Engineering > Electrical & Electronic Engineering
Text - Accepted Version
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